This paper presents an efficient procedure for multi-objective model checking of long-run average reward (aka: mean pay-off) and total reward objectives as well as their combination. We consider this for Markov automata, a compositional model that captures both traditional Markov decision processes (MDPs) as well as a continuous-time variant thereof. The crux of our procedure is a generalization of Forejt et al.'s approach for total rewards on MDPs to arbitrary combinations of long-run and total reward objectives on Markov automata. Experiments with a prototypical implementation on top of the Storm model checker show encouraging results for both model types and indicate a substantial improved performance over existing multi-objective long-run MDP model checking based on linear programming.
@article{arxiv.2010.13566,
title = {Multi-objective Optimization of Long-run Average and Total Rewards},
author = {Tim Quatmann and Joost-Pieter Katoen},
journal= {arXiv preprint arXiv:2010.13566},
year = {2021}
}